Asymptotically cylindrical Calabi-Yau 3-folds from weak Fano 3-folds

Journal Article (Journal Article)

We prove the existence of asymptotically cylindrical (ACyl) Calabi-Yau 3-folds starting with (almost) any deformation family of smooth weak Fano 3-folds. This allow us to exhibit hundreds of thousands of new ACyl Calabi-Yau 3-folds; previously only a few hundred ACyl Calabi-Yau 3-folds were known. We pay particular attention to a subclass of weak Fano 3-folds that we call semi-Fano 3-folds. Semi-Fano 3- folds satisfy stronger cohomology vanishing theorems and enjoy certain topological properties not satisfied by general weak Fano 3-folds, but are far more numerous than genuine Fano 3-folds. Also, unlike Fanos they often contain P 1 s with normal bundle ψ (-1) ⊕ ψ (-1), giving rise to compact rigid holomorphic curves in the associated ACyl Calabi-Yau 3-folds. We introduce some general methods to compute the basic topological invariants of ACyl Calabi-Yau 3-folds constructed from semi-Fano 3-folds, and study a small number of representative examples in detail. Similar methods allow the computation of the topology in many other examples. All the features of the ACyl Calabi-Yau 3-folds studied here find application in [17] where we construct many new compact G2 -manifolds using Kovalev's twisted connected sum construction. ACyl Calabi-Yau 3-folds constructed from semi-Fano 3-folds are particularly well-adapted for this purpose.

Full Text

Duke Authors

Cited Authors

  • Corti, A; Haskins, M; Nordström, J; Pacini, T

Published Date

  • July 15, 2013

Published In

Volume / Issue

  • 17 / 4

Start / End Page

  • 1955 - 2059

Electronic International Standard Serial Number (EISSN)

  • 1364-0380

International Standard Serial Number (ISSN)

  • 1465-3060

Digital Object Identifier (DOI)

  • 10.2140/gt.2013.17.1955

Citation Source

  • Scopus